Amplitude Modulation
RF temporal modulation techniques for communications applications are well known in the art. For example, Principles of Communication Systems, Taub and Schilling [1] is one of many standard electrical engineering textbooks which include sections on amplitude modulation. Chapter 3, “Amplitude-modulation Systems”, the disclosure of which is incorporated by reference herein, provides a good refresher on the theoretical principles and nomenclature used in AM communications. The terms modulating, mixing, heterodyning, baseband, carrier, upper sideband, lower sideband, demodulation, recover, detection, single-sideband, double-sideband, supressed-carrier, narrow-band, square-law detector, and others are well known in the art as described therein, and will be assumed to be defined accordingly, unless exprecessly noted otherwise.
The Art of Electronics, Horowitz and Hill [2] is another standard reference which describes amplitude modulation radio in sections 13.14 and 13.15, the disclosure of both of which are incorporated by reference herein.
Classical Optics
Optical system design techniques for conventional quasi-time-invariant imaging and non-imaging applications are well known in the art. The technical literature has a rich heritage of rules of thumb, first order approximations, technical nomenclature, and fabrication techniques. Standard references include: Fundamentals of Optics, Jenkins and White [3]; Principles of Optics, Born and Wolf [4]; and many others.
With modern computers, and measuring and testing instrumentation, it is now common to correct for higher order time-invariant aberrations and to optimize designs involving many degrees of freedom, including choices of materials, optical element geometry, and systems architectures.
For example, there are a number of excellent computer modeling tools available for analysis and engineering of optical elements and systems, such as: ZEMAX, available from Zemax Development Corp.; CODE-V, available from Optical Research Associates; Optica 3, a Mathematica package available from Wolfram Research, Inc.; and others. U.S. Pat. No. 7,469,202 and US 2009/0143874 to Dowski et al., the disclosure of both of which are incorporated by reference herein, disclose a method for optimizing both optical and digital systems in combination.
Some of these tools do use analysis of modulation in the spatial domain, such as the modulation transfer function (MTF), to model such things as the capability of an optical system to resolve line pairs. However, none of these tools are designed to work with RF or higher temporally modulated wavefronts, i.e., they are designed for time-invariant applications.
Optical Amplitude Modulation
Hereinafter the term “optical amplitude modulation” (OAM) will be understood to mean modulation of the amplitude, power, phase, polarization, frequency, etc. of electromagnetic radiation, modulated at RF, microwave (MW), or terahertz (THz) frequencies in the time domain, so as to produce optical sideband frequencies that propagate at different velocities in a dispersive medium. As will be shown hereinbelow, OAM can include a carrier, but the term will also be understood to apply to suppressed carrier architectures that produce beat notes, e.g., as by interference between two tuned lasers, which act as sidebands.
Such things as spatial amplitude modulation of images by line pairs, and low frequency temporal modulation by such things as chopper wheels, and lock-in amplifiers will be specifically noted, so as not to be confused with the default use of the term OAM, hereinbelow.
Optical Test Methods
Optical test methods are well known in the art for imaging optical components. For example, Optical Shop Testing, Daniel Malacara [5] is a comprehensive reference on the subject, including such topics as interferometry, Ronchi patterns, Moiré, etc. Low frequency phase modulation, or discrete steps in phase, is used in interferometry and Moiré, however these techniques are quasi-time-invariant and do not fit the criteria for OAM as defined hereinabove.
There are no known standard testing methods for optical components as to OAM under the definition hereinabove. Moreover, there are no known standard commercial catalog terms, nomenclature, or specifications to even describe OAM parameters of passive optical components.
Aberrations
Classical time-invariant lens aberrations are well known in the art. Standard references include: Jenkins and White [3], Born and Wolf [4], and others. A good handbook covering aberrations and general optics is chapter 1, “Fundamental Optics”, in the Melles Griot Catalog X [6], the disclosure of which is incorporated by reference herein.
Section 3 of the Melles Griot Catalog X explains wavefront distortion, including how it is defined for product specifications. The first two paragraphs state;                Sometimes the best specification for an optical component is its effect on the emerging wavefront. This is particularly true for optical flats, collimation lenses, mirrors, and retroreflectors where the presumed effect of the element is to transmit or reflect the wavefront without changing its shape. Wavefront distortion is often characterized by the peak-to-valley deformation of the emergent wavefront from its intended shape. Specifications are normally quoted in fractions of a wavelength.        Consider a perfectly plane, monochromatic wavefront, incident at an angle normal to the face of a window. Deviation from perfect surface flatness, as well as inhomogeneity of the bulk material refractive index of the window, will cause a deformation of the transmitted wavefront away from the ideal plane wave. In a retroreflector, each of the faces plus the material will affect the emergent wavefront. Consequently, any reflecting or refracting element can be characterized by the distortions imparted to a perfect incident wavefront.        
It will be shown that the notion of wavefront distortion needs to be extended to distortions of a beat note produced by an ideal modulated wave, and the specification needs to be included in engineering data for an optical product.
Frequency Domain
The use of the Fourier transform in the spatial domain is well known in the optics art for such things as the modulation transfer function (MTF), point spread function (PSF), and optical transfer function (OTF). See Applied Optics, Levi [7] section 3.2, “Spread and Transfer Functions”, the disclosure of which is incorporated by reference herein. Introduction to Fourier Optics, Goodman [8]; is a standard reference which will be referred to in some examples. Linear Systems, Fourier Transforms, and Optics, Gaskill [9] is another.
The Fourier transform in the time domain is well known in the electrical engineering art. For example, The Fourier Transform and Its Applications, Ronald N. Bracewell [10] is a standard reference used by electrical engineers. Electrical engineers are also well versed in the use of the Laplace transform, which is closely related to the Fourier transform. The Laplace transform is well suited to electrical engineering problems as illustrated in Network Analysis, M. E. Van Valkenburg [11].
However, there are no known uses of the Fourier or Laplace transforms in the literature which transform from the time domain to the frequency domain for imaging optical system design, and OAM in particular. While the analysis presented hereinbelow can be developed using either the Fourier or Laplace transforms, the Fourier transform is more familiar to those skilled in the art of optics, and electrical engineers are well versed in both, so the Fourier transform will be used for convenience.
Communications Theory
It will be recognized that optics and communications share much in common. Levi [7], devotes Chapter 3 to, “Communications Theory Aspects of Optical Images”. In the opening paragraph, published in 1968, Levi states;                It seems safe to say that systems using optical images are usually concerned with communications: the transfer or acquisition of information. We do not refer here primarily to communication by modulated light beams but rather to spatially modulated light: “the picture worth a thousand words.”        
The first paragraph of the Introduction to Goodman's book, first published in 1968, states;                Since the late 1930s, the venerable branch of physics known as optics has gradually developed ever-closer ties with the communication and information sciences of electrical engineering. The trend is understandable, for both communication systems and imaging systems are designed to collect or convey information. In the former case, the information is generally of a temporal nature (e.g., a modulated voltage or current waveform), while in the latter case it is of a spatial nature (e.g., a light amplitude or intensity distribution over space), but from an abstract point of view, this difference is a rather superficial one.        
Chapter 10 of Goodman [8] is titled, “Fourier Optics in Optical Communications”. This chapter was added in the 2005 edition of the book. However, the subject matter is drawn to fiber optics and does not address the subject of the invention disclosed herein. It describes the effects of dispersion in the classical terms of group velocity.
Systems and Transforms with Applications in Optics, Papoulis [12] begins the preface, which was also published in 1968, with the following observation;                In recent years, a trend has been developing toward greater interaction between electrical engineering and optics. This is not only because optical devices are used extensively in signal processing, storage, pattern recognition, and other areas, but also because the underlying theory is closely related to the theory of systems, transforms, and stochastic processes. In fact, whereas in system analysis the Fourier integral is an auxiliary concept, in diffraction theory it represents a physical quantity; whereas only a limited class of electrical signals need to be treated as stochastic processes, optical waves are inherently random. The following list illustrates the striking parallels between these two disciplines.        Fresnel diffraction: output of a filter with quadratic phase        Fraunhofer field: Fourier transform        Lens: linear FM generator        Focal plane field: Fourier transform        Contrast improvement: filtering        Apodization: pulse shaping        Coherence: autocorrelation        Michelson interferometer: correlometer consisting of a delay line and an adder        Fabry-Perot interferometer: narrow-band filter        
All three authors actually teach away from the utility of working with optical systems in the time domain. Moreover—over 40 years later—there are no known software tools or standard references that rigorously treat temporally modulated light, or OAM, in combination with imaging optics design and analysis, which this invention addresses. It will be shown that another parallel can be added to Papoulis' observations;                Dispersion: communications theory        
One possible reason for this omission from the literature is that OAM systems are somewhat esoteric and heretofore religated primarily to time-of-flight instrumentation. Another reason is that electro-optical system designs naturally break between the classical optics, and electronics systems disciplines; i.e., the optical engineer takes the optical design to the detector, and the electronics engineer picks it up from the detector. Subtle effects in the optics due to the modulation, such as dispersion, can easily be missed. This invention teaches the effects of OAM and offers suggestions for minimizing negative effects.
Types of Detectors
Most electro-optical systems are designed for imaging, signal collection, spectroscopy, condensing, projection, etc. If an optical signal is temporally modulated, it is usually low frequency—such as chopping to lock-in on an optical signal; or slowly incremented in spatial phase to do phase shift detection, as described in chapter 13 of Optical Shop Testing [5]. Historically, the output of an imaging optical system was a human viewer, film, photoresist, or the like. Nowadays, focal plane arrays, such as CCD and CMOS cameras, are probably the most common sensor at the output end of an optical system. In all of these cases, the output is typically integrated over a period of time, to improve the signal-to-noise ratio, remove 120 Hz flicker of artificial lighting, etc. Since the signal is integrated over time, any higher frequency temporal modulation is removed by low pass filtering of the detector integration period. For systems designed for spectroscopy, temporal modulation is typically not a concern. Optical systems such as these can be designed using classical techniques.
Optical systems designed for signal collection, can use fast single channel detectors which are capable of detecting RF, MW, or THz temporal modulation. In most of these systems, applications such as fiber optics, radar, radio astronomy, satellite dishes, microwave communications, etc., the optical path is fixed, or the entrance pupil is flooded and thus the detector sees a fixed spatial configuration with some variation in the power or phase of the signal communicating information.
It will be shown that optical systems employing curved reflecting surfaces (catoptric systems), such as radio telescopes, optical telescopes, radar systems, etc. do not use dispersive elements, and thus are much simpler to design than refracting (dioptric systems) or combined reflecting and refracting (catadioptric systems) designs. This is explained in some detail in U.S. Pat. No. 6,426,834 to Braunecker et al., the disclosure of which is incorporated by reference herein. Optical systems such as these may benefit from the disclosed invention, but classical techniques may also be sufficient.
Electronic Distance Measurement
There is a small, but significant, field of applications which combine optical systems with fast analog detectors, which are a true hybrid of imaging and communications—which this invention addresses. Electronic Distance Measurement, also called Electromagnetic Distance Measurement (EDM); and absolute distance measurement (to differentiate it from laser interferometry), also called absolute distance meters (ADM); began development in the mid 1960s. The patent literature is rich with inventions in EDM. U.S. Pat. No. 3,365,717 to Holscher; U.S. Pat. No. 3,508,828 to Froome et al.; and U.S. Pat. No. 3,619,058 to Hewlett et al., the disclosure of all three of which are incorporated by reference herein, were among the early US patents in the field.
EDM presents unique optical challenges, which will be explained in detail. Electromagnetic Distance Measurement, Burnside [13], is a good introduction to the fundamentals. Selected Papers on Laser Distance Measurements, Bosch and Lescure [14] is a good collection of the non-patent literature. Electronic Distance Measurement, Rüeger [15], presents the theory of operation of many EDM instruments.
In the opening paragraph, Rüeger states:                Historically, the development of electro-optical distance meters evolved from techniques used for the determination of the velocity of light. Fizeau determined the velocity of light in 1849 with his famous cog-wheel modulator on a line of 17.2 km length: Light passed through the rotating cogwheel, traveled to a mirror at the end of the line, was reflected and returned to the wheel where the return light was blocked off by the teeth at high revolutions of the wheel. Fizeau's experiment employed for the first time the principle of distance measurement with modulated light at high frequencies.For details of Fizeau's experiment, see Chapter 1 of Jenkins and White[3], the disclosure of which is incorporated by reference herein.        
Commercially available EDM instruments are typically combined with two angle measurements, as with a theodolite, and used in high precision surveying instruments such as surveying total stations, also known as tacheometers; laser trackers; laser scanners; and the like. These instruments are available from companies such as Leica Geosystems, FARO Technologies, Topcon, Sokkia, Trimble, Pentax, API, and others. EDMs are also available in consumer priced, lower precision, distance only instruments available in the hardware store. While the prior art deals with the bulk effects of dispersion in the atmosphere, to correct the speed of light for temperature, humidity, and pressure; no known prior art deals with dispersion within the instrument optical design, or inhomogeneities of the wavefront across the plane of the beam, due to dispersion of the optical elements, in particular.
One EDM design is disclosed in U.S. Pat. No. 5,455,670 ('670) to Payne et al., the disclosure of which is incorporated by reference herein. In '670, a laser is modulated at 1500.000 MHz and the reflected laser beam phase is detected by a PIN detector. The detected signal is mixed with a coherently generated local oscillator at 1500.001 MHz to produce a 1 kHz IF, which is related to the phase of the 1500 MHz modulation signal, and the distance to a reflective target. Many other architectures, including polarization modulation, pulsed, and chirped systems, are in use and are well known in the art. Most EDMs use hollow retroreflectors or solid glass corner cubes for the target to be measured, as is well known in the art. U.S. Pat. No. 7,101,053 to Parker, the disclosure of which is incorporated by reference herein, provides a good survey of the topic.
In the development of the '670 invention, the Model PSH97, it was observed that the apparent distance, or phase of the detected beat note signal, was slightly dependent on the size of the return beam. For example, if an iris was placed at the objective lens, the measured distance changed slightly as the iris was opened or closed. It was also observed that the apparent distance was slightly dependent on which part of the expanded beam was retroreflected back to the instrument. For example, the apparent distance was found to be slightly dependent on the pointing of the beam, i.e., if the beam was not centered on the retroreflector, the distance changed with the pointing. This was also observed in experiments with a Topcon total station. The source of the error was not determined in the course of the development of the instruments for the National Radio Astronomy Observatory (NRAO), Robert C. Byrd Green Bank Telescope (GBT) project. Subsequent thought and investigation as to the source of the error gives rise to the instant invention.
Other Preferred Embodiments
While modulation of light at microwave frequencies is well known in the art, rapid advances have been made in the generation of terahertz (THz) waves, which span the spectrum between microwaves and infrared radiation. For example, U.S. Pat. No. 7,684,023 to Kang et al., discloses Apparatus and method for generating THz wave by heterodyning optical and electrical waves. It will be recognized that the invention will have application for these wavelengths also.
While radio telescopes employ catoptric main reflectors, many receivers employ dielectric lenses to correct for aberrations of the main reflector, subreflector, or other optical elements, and thus temporally modulated signals, such as pulsars (rotating neutron stars that emit light pulses at frequencies up to ≈1 kHz) may be subject to additional dispersion due to the optics. This could also be a source of error for very long baseline interferometry (VLBI) as explained in Interferometry and Synthesis in Radio Astronomy, Thompson, Moran, and Swenson [16].
While the invention will be illustrated by preferred embodiments and figures related to EDM, the invention is only limited by the claims, and other embodiments employing the spirit of the invention will be recognized by those skilled in the art. For example, the same principles may be applied to instruments designed as refractometers to measure index of refraction of materials, chemical composition, temperature, humidity, pressure, atmospheric turbulance refractivity structure constant Cn2, mechanical vibrations, or the like.